Yes

A wizard can use False Life and Life Transference to heal someone else.
From OP:

So my idea is in the first turn cast False Life (I already have the spell) to get temporary HP, then cast Life Transference to "send" that "self-healing" to another PC, and finally use False Life or Vampiric Touch (I can learn it) to recover some HP (temporaly or real ones). But I am not sure if that is possible.

Long answer:

Temporary Hit Points:

When you have temporary hit points and take damage, the temporary hit points are lost first, and any leftover damage carries over to your normal hit points.

Vampiric Touch:

Make a melee spell Attack against a creature within your reach. On a hit, the target takes 3d6 necrotic damage, and you regain hit points equal to half the amount of necrotic damage dealt.

By RAW a character which uses Life Transference or is attacked by Vampiric Touch spell would eliminate the target's temporary hit points first with any additional damage caused to normal HP after it, the spell does not care if the damage dealt was to real (permanent) or 'fake' (temporary) HP and still restores half of the total necrotic damage dealt.

Being immune or resistant to necrotic damage matters for the Vampiric Touch or Life Transference damage and regained HP, the HP being temporary doesn't.

Unless your GM house-ruled this then indeed you can turn temporary HP into actual, real permanent HP as by the book.

Life Transference is not different from how necrotic damage is handled. You should by RAW/RAI be able to cast False Life on yourself then transfer real HP to the one in need. Necrotic damage is just like fire or ice damage which one could have resistance or immunity against but it does not ignore temporary HP. No powerful divine healing or such is required just because it is necrotic instead of ice or piercing damage (as example).

You do it willing over yourself, so it surpass any effect, shield (I think that includes temporary HP)"

"Necrotic damage always surpasses temporary HP"

"If I want (but I don't), necrotic damage could rotten your body, or need high level healing spells"

These are not by RAW or RAI, no such rules exists, Either these are house rules or a big misunderstanding about necrotic damage, a GM mistake.

If the GM indeed rules that necrotic damage ignores temporary HP and shields (which makes no sense) then the use of that form of damage just greatly increased in your game, making magical weapons with that type of bonus damage, or the spell Vampiric Touch a more potent offensive option. If necrotic damage ignores in your GM's house rules a shield ask if it also ignores a full plate.

Yes, you can use the ability.

Relentless Endurance states:

Relentless Endurance. When you are reduced to 0 hit points but not killed outright, you can drop to 1 hit point instead. You can’t use this feature again until you finish a long rest.

Since the spell says nothing about killing you outright if this damage reduces you to 0 hit points, and there's no mention of the source of the damage, yes, the ability would activate when you take damage from Life Transference, which states the following:

You sacrifice some of your health to mend another creature’s injuries. You take 4d8 necrotic damage, and one creature of your choice that you can see within range regains a number of hit points equal to twice the necrotic damage you take.

There is no mention of something along the lines of "this damage can't be reduced in any way", as the Wish spell does:

Wish. [...] The stress of casting this spell to produce any effect other than duplicating another spell weakens you. After enduring that stress, each time you cast a spell until you finish a long rest, you take 1d10 necrotic damage per level of that spell. This damage can’t be reduced or prevented in any way.

Therefore, since spells in D&D 5e only do what they say, yes, you can use the spell in this way (at least according to RAW - your DM might decide otherwise).

The creature heals whatever you rolled on your 4d8 (or more, depending on the spell level).

To answer your question about how much healing is applied, this is what happens:

You cast the spell -> you take 4d8 damage + the creature of your choice within range regains the exact same amount -> you are reduced to 0 HP -> your ability activates, so you have 1 HP instead.

There's a difference between the amount damage you take, and the amount that your hit points are effectively reduced. On page 196 of the PHB, the section Hit Points states:

A creature’s current hit points (usually just called hit points) can be any number from the creature’s hit point maximum down to 0.

Therefore, if you're e.g. at 10HP, cast the spell and roll 17 damage on the 4d8, you would be at -7 HP. However, your hit points can only be between 0 and max, so you drop to 0 instead - but you still took 17 damage.

The difference between damage taken and HP lost is further supported by the section about instant death, PHB p. 197:

Instant Death Massive damage can kill you instantly. When damage reduces you to 0 hit points and there is damage remaining, you die if the remaining damage equals or exceeds your hit point maximum.